Problem 10-15 NPV Break-Even (LO2) Modern Artifacts can produce keepsakes that w

Question

Problem 10-15 NPV Break-Even (LO2)

Modern Artifacts can produce keepsakes that will be sold for $100 each. Nondepreciation fixed costs are $1,300 per year and variable costs are $70 per unit.

If the project requires an initial investment of $4,000 and is expected to last for 5 years and the firm pays no taxes. The initial investment will be depreciated straight-line over 5 years to a final value of zero, and the discount rate is 12%. What are the accounting and NPV break-even levels of sales? (Do not round intermediate calculations. Round your answers to the nearest whole number.)

What will be the accounting and NPV break-even levels of sales, if the firm's tax rate is 30%? (Do not round intermediate calculations. Round your answers to the nearest whole number.)

Modern Artifacts can produce keepsakes that will be sold for $100 each. Nondepreciation fixed costs are $1,300 per year and variable costs are $70 per unit.

Explanation / Answer

Annual depreciation = 4000/5 = 800

Contribution margin per unit = sales-variable cost = 100-70=$30/unit

a. Let acccounting breakeven units be X

So accounting profit each year = 30X-1300 (fixed cost)-800 (depreciation) = 30X-2100

For accounting breakeven, 30X-2100 = 0, which means X=70 units

Net cashflow each year = profit+depreciation = 30X-2100+800 = 30X-1300 = C

NPV = C/(1+10%)^1 + C/(1+10%)^2 + C/(1+10%)^3 + C/(1+10%)^4 + C/(1+10%)^5 = 4000 at breakeven

This means C = 1055.19

But C = 30X-1300

So 30X-1300 = 1055.19

So X = 78.51 units

To summarize, accounting breakeven units = 70 units, and NPV breakeven units = 78.51 units

b. Let acccounting breakeven units be X

So accounting profit before tax each year = 30X-1300 (fixed cost)-800 (depreciation) = 30X-2100

Accounting profit after tax each year = (30X-2100)*(1-30%) = 21X-1470

For accounting breakeven, 21X-1470 = 0, which means X=70 units

Net cashflow each year = profit+depreciation = 21X-1470+800 = 21X-670 = C

NPV = C/(1+10%)^1 + C/(1+10%)^2 + C/(1+10%)^3 + C/(1+10%)^4 + C/(1+10%)^5 = 4000 at breakeven

This means C = 1055.19

But C = 21X-670

So 21X-670 = 1055.19

So X = 82.15 units

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